If the function f(x)=x^4-62 x^2+ax+9 attains its local maximum value…

$f(x)=x^4-62 x^2+a x+9$

local maxima is at x = 1

$f'(x)=4 x^3-124 x+a$

so $f'(1)=0=4-124+a$   (at maxima / minima slope of function is null)

so  a = 124 - 4

so  a = 120